Greystones' Paul Dunne kept himself in the mix at the DP World Tour Championship courtesy of two second-round eagles in Dubai.
The British Masters champion finished three shots behind overnight leader Matthew Fitzpatrick, who carded a second consecutive 67.
Dunne signed for a 70 to move to seven under par, with a round which included two eagles, two birdies and four bogeys.
Shane Lowry, meanwhile, kept himself in contention the mix with a two-under-par 70, five shots off the lead and tied for 15th with six others.
Masters champion Sergio Garcia, the only other contender in the Race, is a shot behind Fleetwood and three adrift of Justin Rose after his 69.
Ronnie O'Sullivan lined up a Shanghai Masters final against Judd Trump after seeing off John Higgins in yesterday's semi-final.
Five-time world champion O'Sullivan wrapped up the 6-2 win with a break of 123 - the highest in the match - to clinch victory.
Scotland's Higgins narrowly missed out on the chance to regain a foothold in the contest at 4-2 down when the seventh frame hinged on the final black.
Trump awaits O'Sullivan in the final after he defeated close friend Jack Lisowski 6-3 in the other semi-final.
At 2-2, Bristolian world number three Trump fired off a break of 105 to win the fifth but was again pegged back, before he won three straight frames to book his final place.
"At 3-3 he was looking the better player so I had to dig in," Trump said.
Valentine Holmes scored a record five tries as Australia continued their imperious World Cup title defence with a 46-0 thrashing of Samoa in the quarter-finals in Darwin.
Co-hosts New Zealand, who were stunned by Tonga in their final pool match, face the Fijians in Wellington today. The Tongans take on Lebanon in today's other quarter-final to decide who will play the second semi-final against England or Papua New Guinea, who meet tomorrow.